Sub-THz wireless transmission based on graphene-integrated optoelectronic mixer

Optoelectronics is a valuable solution to scale up wireless links frequency to sub-THz in the next generation antenna systems and networks. Here, we propose a low-power consumption, small footprint building block for 6 G and 5 G new radio wireless transmission allowing broadband capacity (e.g., 10–100 Gb/s per link and beyond). We demonstrate a wireless datalink based on graphene, reaching setup limited sub-THz carrier frequency and multi-Gbit/s data rate. Our device consists of a graphene-based integrated optoelectronic mixer capable of mixing an optically generated reference oscillator approaching 100 GHz, with a baseband electrical signal. We report >96 GHz optoelectronic bandwidth and −44 dB upconversion efficiency with a footprint significantly smaller than those of state-of-the-art photonic transmitters (i.e., <0.1 mm2). These results are enabled by an integrated-photonic technology based on wafer-scale high-mobility graphene and pave the way towards the development of optoelectronics-based arrayed-antennas for millimeter-wave technology.


I. DEVICE DESIGN AND SIMULATION A. Optoelectronic mixing
The sub-THz transmitter presented in the main text is based on a graphene optoelectronic mixer.The operating principle of the device relies on the possibility of modulating the electrical conductivity of a graphene layer by means of an optical field.Let's consider a graphene layer in dark conditions, with conductivity σ dark = 1/ρ dark , being ρ the resisitivity of the material.As detailed in I D, the coupling of the material with an optical field results in a change of the electronic temperature T e and, consequently, of the chemical potential µ c [1].This translates in a change of the electrical conductivity [1], so that in illumination conditions one has: Thus, the conductance of a graphene layer of length L and width W under homogeneous illumination is: And the corresponding resistance is: Being R dark = 1/G dark and ∆R = 1/∆G.This corresponds to the parallel of two resistors.Supplementary Figure 1a takes up the scheme of the device presented in Fig. 3 of the main text.In our experiment, the graphene layer is embedded inside an electrical coplanar waveguide, which is a transmission line with characteristic impedance Z 0 = 50Ω (as detailed in I B), fed by a voltage generator V in with output impedance R S = 50Ω, and connected to an antenna with impedance R L = 50Ω.The equivalent circuit of the graphene layer is deduced from equation S.3, as shown in the zoom of Supplementary Figure 1a, where the graphene-metal contact resistance R C is also included.The resulting circuit is shown in Supplementary Figure 1b.The circuit model is purely resistive and describes the device including metal/graphene contact resistance.This model completely keeps the behavior of the device and is sufficient to describe the optoelectronic mixing operation in the considered frequency range (< 100 GHz).The graphene intrinsic dynamics limiting the frequency response of our device would be observed at frequencies well above our experiment (∼ 500 GHz) as very recently shown [2] and therefore is not included in the model.Besides this, the passive RF circuitry embedding the device could lead to bandwidth degradation if not well designed.As shown in Sec.B, the transmission line embedding our device is a coplanar waveguide designed to have a characteristic impedance of 50 Ω in the whole operating frequency range.Since the CPW characteristic impedance coincides with the output impedance of the voltage generator, it is not included in the lumped model.By defining R A = R S + R C + R L , the output voltage V out can be expressed as: The device acts as a frequency mixer when V in and ∆R are time-varying.More specifically, let V in be an electrical sinusoidal signal of frequency f ele : and ∆R be modulated at frequency f LO by a time-varying optical signal.Thus: Where the constant level δσ accounts for the conductivity change induced by the mean optical power.To analytically visualize the mixing product, 1 in S.4 can be approximated as: while 2 can be approximated as: Thus V out can be written as: the second term in S.9 contains the product between the two time-varying signals, which gives: We used the G-OEM to implement the transmitting part of the wireless link.Nevertheless, from S.9 it follows that the G-OEM can also be used as down-converter in a sub-THz receiver.To evaluate the conversion efficiency of the G-OEM, we solved the circuit represented in Supplementary Figure 1b using equation S.4, that is, without using the approximations in equations S.7 -S.9.Moreover since the optical power coupled to the graphene layer is not homogeneously distributed along the channel (see I C, and I D), we calculated the conductance G dark and G light by integrating the spatial-dependent conductivity σ(x, y) derived from simulations, as detailed in section I D.
It is worth noting that this device does not need any DC bias voltage applied to the graphene channel, when operated as optoelectronic mixer.This is a substantial difference compared to graphene-based photobolometers operating as photodetector, which are affected by high power consumption due to the need of DC current.

B. RF design and simulation
With reference to Supplementary Figure 1a-b, to match the output impedance of the voltage generator R S = 50Ω and the output impedance of the load R L = 50Ω represented by the antenna in the transmission system, the coplanar waveguide (CPW) embedding the graphene layer has been designed to have a characteristic impedance Z 0 = 50Ω.Supplementary Figure 2 shows the top view of the CPW, and its cross section along the cut line indicated in red.The quasi-TEM electromagnetic mode is simulated using a commercial software (Comsol Multiphysics).The target impedance has been obtained for S = 74µm and gap = 17.5µm.Supplementary Figure 2: CPW Simulation and design.Top view of the CPW and its cross-section with the quasi-TEM electromagnetic mode, at the level of the red cut line.The device has been fabricated using the dimensions indicated in the figure, which give a characteristic impedance Z 0 ∼ 50Ω

C. Optical absorption calculation
Light absorption allowing optoelectronic mixing takes place at the level of the bottom graphene active layer.Nevertheless, a fraction of the optical power is absorbed by the top graphene layer and by the metal contacts.This portion represents the insertion loss of the device.To evaluate the actual optical power that is absorbed by the graphene bottom layer (that is, the portion of power responsible of the graphene conductivity change), we adopted the same simulation procedure used in the Supplementary Information of [3]: we simulated the TE waveguide mode profile of the waveguide coupled to the active graphene layer.We then calculated the optical absorption per unit length α active layer from the imaginary part of the effective refractive index.We then simulated the whole structure, comprising the top graphene and metal contacts, and extracted again the optical absorption per unit length α total .By defining: The absorbed power in the active layer along the optical mode propagation direction is [3]: L a (S.12) where P in is the input optical power, P y is the Pointing vector component along the propagation direction, L a is the absorption length, defined by: Being P opt (y) the optical power propagating along the structure at the coordinate y, undergoing exponential decay due to absorption [3,4]: The absorbed power in the active layer P (x, y) is then used as heat source to calculate the electronic temperature along the graphene channel, as detailed in I D. The profile of P (x, y) is shown in Supplementary Figure 3.The absorbed power density scale refers to an input power of 1mW .
Supplementary Figure 3: G-OEM optical power absorption simulation.Simulated absorbed optical power density, in the active graphene layer (for an input power of 1 mW), which acts as heat source for hot electrons.The waveguide region is evidenced in white, as well as the metal contacts regions, between which the graphene active layer is present

D. Conductivity calculation
As discussed in I A, the G-OEM working principle is based on the change in the electrical conductivity of the graphene layer under optical excitation.The electrical conductivity can be expressed as [1,5]: where ω is the angluar frequency at which electrons drift in the material according to the Drude transport picture, µ c the chemical potential, T e is the electronic temperature, Γ the transport scattering rate and D the Drude weight.For a two-dimensional Dirac Fermions gas, this last reads [1]: Where e is the elementary charge, ℏ is the reduced Planck constant, k B the Boltzmann constan.The expression of Γ in S.15 depends on the microscopic physical mechanisms limiting charges transport, which changes depending on graphene quality and on its electrostatic environment [6,7].We phenomenologically model Γ assuming constant mobility µ as a function of the carriers chemical potential µ c .In this case, the transport scattering rate can be deduced from [8]: The angular frequency in the sub-THz range is ∼ 10 11 rad/s, while Γ lies in the range ∼ 10 12 − 10 13 rad/s [9].We thus neglect the frequency dependence in equation S. T e,room is the electrons temperature in dark conditions, which coincides with the lattice temperature.T e,hot is the hot electrons temperature due to light coupling.The temperature dependence of the chemical potential µ c (T e ) is found by numerical inversion of the charge carriers conservation formula [10]: Being v F the Fermi velocity, Li 2 , the dilogarithm function [10], V GS the top gate voltage.α is 1 or 2, for respectively, metallic or graphene gates [10,11].In our case, α = 2. C ox = ϵϵ hBN t hBN is the geometrical capacitance, which depends on the hBN dielectric constant ϵ hBN and on its thickness t hBN .ϵ is the vacuum permittivity.We then account for the effect of electrons-holes puddles by substituting the chemical potential found in equation S. 19 with [1]: Where µ puddles is calculated from the charge inhomogeneity n 0 at the charge neutrality point [10]: In our sample, µ puddles ∼ 0.033eV , since n 0 ∼ 8 • 10 10 (see main text).To get the spatial profile of the electronic temperature under optical excitation, we solved the heat equation.For high mobility samples this reads [5]: The left hand of equation S.22 contains two cooling terms: the first is related to the electronic heat conduction LσT e , defined by the Wiedeman-Franz law, where 3e 2 is the Lorenz number, σ is the electrical conductivity.The second term Q = Ce τ cool (T e − T ph ) is the energy transfer rate associated to the hyperbolic phonon polariton radiative cooling occourring in hBN-encapsulated graphene samples [12].T ph is the phonon temperature.We assume T ph = T room = 300K.C e is the specific heat of graphene.This quantity is usually approximated, depending on the operating conditions.Specifically [5]: Being ζ the Riemann zeta function.In our operating conditions E F k B T e is comparable to 1. Putting the first formula of S.23 in eq.S.22 overestimates the electrons temperature, while the use of the second formula of S.23 leads to an underestimation of the electrons temperature far from the charge neutrality point (G-OEM operating condition).We thus explicitly calculate the specific heat using the general formula [13]: Where E is the energy of each charge particle, E F = µ c (T = 0K) is the Fermi level, f is the Fermi-Dirac distribution and g(E) 2 |E| is the density of states in graphene [10].In [14] authors calculated τ cool ∼ 2ps for T ph = 300K in high doping, weak-heating regime (µ c ≫ k B T , T e ∼ T ph ).In our experiment T e can be significantly higher than T ph , since we attain optical powers inducing T e approaching 1000K.Nevertheless, the same reference ( [14]) compares the calculation in weak-heating regime with experimental data obtained in strong heating regime (T e ≫ T ph ), revealing very small deviation from the two conditions.Based on these considerations, we used τ cool ∼ 2ps.The right hand of equation S.22 is the heat source, represented by the optical power absorbed along the graphene channel, defined by equation S.12.S.22 does not include the supercollisions cooling term [15], as it is predominant only in low mobility samples [9,15].We obtained the temperature profile along the graphene channel using a finite-element commercial solver (Comsol Multiphysics), and consequently extracted the conductivity in light and dark conditions using S.15.Supplementary Figure 4a shows the electronic temperature profile T e, while Supplementary Figure 4b shows the chemical potential µ c (T e) along the graphene channel, at a gate Voltage V G − V CN P = 2.3V , for a power input of 20 mW.These two quantities were then used to extract ∆σ, as defined in S.18.This last is shown in Supplementary Figure 4c.Because of the spatial dependence of σ light , σ dark , ∆σ, the values G light and G dark (defined in S.3 in the case of homogeneous illumination) where actually calculated by numerical integration over the space coordinates: where L = 4µm is the length of the graphene channel (electrical transport direction) and W = 50µm is the width.The gate dependent change in conductivity under illumination ∆G(V ) is shown in Supplementary Figure 5.The simulation well reproduces the typical photoconductivity curve of a biased graphene detector [16]: near the charge neutrality point, the material behaves similarly to a typical semiconductor (photoconductive regime) [1,17] while at higher doping a conductivity decrease takes place due to carrier heating, analogously to metals (photobolometric regime) [1,17].

E. Upconversion efficiency
The upconversion efficiency of the G-OEM was calculated in the following way: we first solved the circuit in Supplementary Figure 1.V in in equation S.5 was set to 632.36mV .This is the voltage applied by a power generator delivering a maximum power P in = 0dBm (1 mW) in matched conditions [18], i.e. when a 50Ω load is directly connected to the generator.We then calculated V out from S.4, with ∆R defined by equation S.6.Finally, we computed the power spectral density of V out across the load resistor R L = 50Ω: Being F the Fourier transform operator.We extracted the Fourier component at f LO + f ele , that is the upconverted power P out = P out (f LO + f ele ).We define the upconversion efficiency as: In the calculation we used an input power P in = 0dBm, thus P conv[dB] = P out [dBm] .Supplementary Figure 6 shows the plot of the simulated upconversion efficiency for an input optical power of 20 mW, as a function of V G .The conversion efficiency has a maximum of 41dB in the bolometric regime (high doping) for V G − V CN P = 1.4.This gate voltage defines the operating point of the G-OEM.We experimentally found an optimal EVM for V G − V CN P = 2.3V , with upconversion efficiency of ∼ 44dB.The difference between simulation and experiment can be attributed to non-idealities that are not taken into account in the simulation, e.g. the room temperature set to 300K, and Joule heating induced by the electrical power which actually changes the electrons and phonons rooom temperature.From simulations, we get the best upconversion efficiency at the charge neautrality point, while in our experiment we got poor EVM for V G = V CN P .This can be attributed to higher electrical reflections compared to the high doping Supplementary Figure 5: Simulated graphene channel change in conductance (∆G) under illumination, vs gate voltage.The simulation is performed for an input optical power of 20 mW.
operation, due to the high impedance mismatch between the 50Ω generator and the circuit when the graphene electrostatic doping is low.
Upconverted RF power (dBm) Supplementary Figure 6: Simulated upconversion efficiency vs Gate voltage, for an input optical power of 20 mW To increase the wireless link distance and datarate (i.e., larger bandwidth and higher order modulation formats), the signal-to-noise ratio (SNR) has to be optimized.In the main text, we indicate some optimization for the wireless link system, which are the use of higher gain antennas, more performing digital-to-analog converters (also discussed in IV) and lower noise electronics at both the receiver and the transmitter level.Besides system optimization, the SNR can be improved acting on the design of the G-OEM itself.The parameter to be optimized is the up-conversion efficiency, which is related to the device geometry and to the graphene quality.Concerning geometry, our design choice was tailored considering a contact resistance value in the range 1 − 2KΩµm.If the contact resistance is lower, it is convenient to reduce the active area footprint.Considering a contact resistance of ∼ 500Ωµm, achievable at the wafer scale level (although currently only achievable at high carrier concentration level compared to the operating point of our G-OEM) [19], the graphene channel length and width can be reduced from L = 4µm to L = 2µm and from W = 50µm to W = 25µm.We simulated this geometry using a uniformly distributed absorbed optical power along the channel.This condition can be achieved e.g. by coupling light from both sides of the waveguide underneath the graphene channel.In this condition, we obtain P conv ∼ −33dB, with performance boost of ∼ 11dB compared to the experimental value obtained with the present design.A further improvement could be obtained using plasmonic enhancement, which greatly improves the internal photoresponsivity [20].
Concerning graphene quality, we used hBN-encapsulated graphene to suppress super-collisions cooling [15] and obtain higher hot electrons temperatures and consequently higher responsivities compared to low mobility samples.The change in conductivity of graphene photobolometers is fundamentally due to a reduction of impurity and lattice disorder screening while rising the electronic temperature [9], which induces a mobility reduction, thus a conductivity decrease.To quantitatively evaluate the performance of a G-OEM based on low mobility graphene, we simulated the device using a mobility of 4000 cm 2 V −1 s −1 , with charge carrier inhomogeneity n 0 = 6 • 10 11 cm −2 .These are typical values of graphene on SiO 2 [9].In this conditions, long-range Coulomb scattering dominates transport, and supercollisions are the major pathway for hot electrons cooling [15].We thus included this contribution in the heat equation and removed the hyperbolic phonon polariton radiative cooling term which only takes place in hBN-encapsulated graphene [12,14].In this case, the heat equation reads [15]:

28)
Being A = 9.62 4g(µc) ℏk F l k 3 B [15, 21], , with k F the Fermi wave vector.The result is shown in Supplementary Figure 7.The upconversion efficiency is ∼ −55 dB in the photobolometric region, which is > 25 fold decrease compared to the simulation using high mobility graphene and the current design.The dependence of carriers mobility against temperature in low mobility samples, in which the transport is dominated by long-range Coulomb scattering, has been widely studied both theoretically and experimentally [9].In hBN-encapsulated high mobility graphene, the dominant cooling pathways are hyperbolic phonon polariton radiative cooling and electronic heat conduction [12,14], while transport is dominated by random strain disorder [6,7].This one has two contributions, i.e., random scalar potential and random gauge potential [6,7].The first contribution leads to temperature-dependent mobility, while the second doesn't [6,7,22].Therefore, even if a further increase of mobility could lead to higher hot electrons temperatures, this may not correspond to a net enhancement of conductivity change.Future experimental studies on ultra-high mobility graphene bolometers could clarify this.

II. WIRELESS LINK EXPERIMENTAL SETUP
The experimental setup of the wireless link is shown in Supplementary Figure 8.The TX is composed by the G-OEM performing upconversion, a sub-THz amplifier and a TX antenna.The RX is composed by a receiving antenna and a commercial downconverter.The two horn antennas are 2-m far from each other.

III. CONVERSION EFFICIENCY VS OPTICAL LOCAL OSCILLATOR POWER
As a complement to the RF characterization presented in the main text, we measured the conversion efficiency as a function of the optical LO power, while keeping a fixed electrical IF input power of 0 dBm.The result is shown in Supplementary Figure 9 .The slope of the experimental curve is 1.9 dB/dB, consistent with the theoretical expected value of (2 dB/dB) that is the usual linear optical power detection regime.Indeed, in the linear regime, the photocurrent is proportional to the optical power, and the associated photo generated electrical power is the square of the photocurrent.Thus, there is a square law between the coupled optical power and the photogenerated electrical power.For 13 dBm OL power, a saturation behavior can be inferred, consistent with Fig. 8b in the main text.

Figure 1 :
Circuital model of the G-OEM.a) Circuital representation of a graphene resistor, with ∆R being the resistance contribution under light excitation.b) Circuital model of the graphene optoelectronic mixer including an input voltage generator, the contact resistance and the load resistor 15.The optical power coupled to the grpahene channel induces a change in T e and in µ c so that the change in conductivity ∆σ in equation S.1 can be expressed as: ∆σ = σ dark − σ light = D(µ c (T e,room ), T e,room ) π(Γ(µ c (T e,room ), T e,room )) − D(µ c (T e,hot ), T e,hot ) π(Γ(µ c (T e,hot ), T e,hot )) (S.18)

Supplementary Figure 4 :
Device Simulation.spatial map of: (a) Temperature, (b) Chemical potential(c) ∆σ.The simulation is performed for an input optical power of 20 mW, V G − V CN P = 2.3V .

Supplementary Figure 7 :
Simulated upconversion efficiency vs Gate voltage for low mobility sample (µ = 4000cm 2 V −1 s −1 , n 0 = 6 • 10 11 cm −2 )for an input optical power of 20 mW Supplementary Figure8: wireless link setup, comprising the Treansmitter and receiver sections.At the transmitter, a baseband QPSK signal is generated and connected to the G-OEM chip.This last is visible in the microscope image on the screen.The output of the G-OEM is connected to the TX amplifier.The TX antenna sends the upconverted sub-THz signal to the RX antenna, connected to the commercial RX downconverter.